Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 574-591 |
| Seitenumfang | 18 |
| Fachzeitschrift | Computer Methods in Applied Mechanics and Engineering |
| Jahrgang | 346 |
| Publikationsstatus | Veröffentlicht - 13 Dez. 2018 |
Abstract
We propose a method to obtain diagonal mass matrices for NURBS-based approximation spaces by a “dual lumping” method. The use of lumped mass matrices is of great importance in elastodynamics problems, as they can be employed in explicit time integration schemes which do not require the solution of a linear system. In finite elements, several well-established methods, such as row-sum, diagonal scaling, or nodal quadrature methods have been used to obtain lumped mass matrices for different applications. However, for higher-order and higher continuity approximation spaces such as those derived from NURBS, these approaches have only limited (second-order) accuracy. In this work, we derive a dual basis which has optimal approximation and dispersion properties, while maintaining local support. The dual space has discontinuities at the element boundaries (knots) and it is used to provide the test functions in the context of a Petrov–Galerkin method. This results in a general framework for the study of lumped mass matrices which can be employed in explicit time integration schemes with high-order accuracy. Numerical experiments are presented to demonstrate the applicability of the method to problems with smooth solutions as well as to wave propagation problems with reduced regularity.
ASJC Scopus Sachgebiete
- Ingenieurwesen (insg.)
- Numerische Mechanik
- Ingenieurwesen (insg.)
- Werkstoffmechanik
- Ingenieurwesen (insg.)
- Maschinenbau
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
- Informatik (insg.)
- Angewandte Informatik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 346, 13.12.2018, S. 574-591.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Isogeometric analysis for explicit elastodynamics using a dual-basis diagonal mass formulation
AU - Anitescu, Cosmin
AU - Nguyen, Thanh Chuong
AU - Rabczuk, Timon
AU - Zhuang, Xiaoying
PY - 2018/12/13
Y1 - 2018/12/13
N2 - We propose a method to obtain diagonal mass matrices for NURBS-based approximation spaces by a “dual lumping” method. The use of lumped mass matrices is of great importance in elastodynamics problems, as they can be employed in explicit time integration schemes which do not require the solution of a linear system. In finite elements, several well-established methods, such as row-sum, diagonal scaling, or nodal quadrature methods have been used to obtain lumped mass matrices for different applications. However, for higher-order and higher continuity approximation spaces such as those derived from NURBS, these approaches have only limited (second-order) accuracy. In this work, we derive a dual basis which has optimal approximation and dispersion properties, while maintaining local support. The dual space has discontinuities at the element boundaries (knots) and it is used to provide the test functions in the context of a Petrov–Galerkin method. This results in a general framework for the study of lumped mass matrices which can be employed in explicit time integration schemes with high-order accuracy. Numerical experiments are presented to demonstrate the applicability of the method to problems with smooth solutions as well as to wave propagation problems with reduced regularity.
AB - We propose a method to obtain diagonal mass matrices for NURBS-based approximation spaces by a “dual lumping” method. The use of lumped mass matrices is of great importance in elastodynamics problems, as they can be employed in explicit time integration schemes which do not require the solution of a linear system. In finite elements, several well-established methods, such as row-sum, diagonal scaling, or nodal quadrature methods have been used to obtain lumped mass matrices for different applications. However, for higher-order and higher continuity approximation spaces such as those derived from NURBS, these approaches have only limited (second-order) accuracy. In this work, we derive a dual basis which has optimal approximation and dispersion properties, while maintaining local support. The dual space has discontinuities at the element boundaries (knots) and it is used to provide the test functions in the context of a Petrov–Galerkin method. This results in a general framework for the study of lumped mass matrices which can be employed in explicit time integration schemes with high-order accuracy. Numerical experiments are presented to demonstrate the applicability of the method to problems with smooth solutions as well as to wave propagation problems with reduced regularity.
KW - Bézier extraction
KW - Dual-basis
KW - Elastodynamics
KW - Isogeometric analysis
KW - Lumped mass
UR - http://www.scopus.com/inward/record.url?scp=85059037477&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2018.12.002
DO - 10.1016/j.cma.2018.12.002
M3 - Article
AN - SCOPUS:85059037477
VL - 346
SP - 574
EP - 591
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -